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A fiber-reinforced mesoscale constitutive model of tympanic membrane considering anisotropic deformation

考虑各向异性变形的人耳鼓膜纤维增强细观本构模型

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Abstract

The tympanic membrane (TM), located at the end of the ear canal, is a collagenous multi-layer soft tissue membrane with fibers highly aligned in radial and circumferential orientations. This unique multi-layer fiber ultrastructure makes TM’s mechanical behavior display both anisotropy and nonlinearity, which is important in sound transmission. However, the constitutive model of TM which includes both features has not been proposed. In this study, we develop a fiber-reinforced mesoscale constitutive model of TM which captures both anisotropic and nonlinear elastic mechanical behaviors. The TM is considered a continuum fiber-reinforced composite with two families of collagen fibers. Its overall properties are built up by integrating its heterogeneous material properties through the thickness. The homogenized mechanical properties are assumed to be uniformly distributed through TM’s thickness and superposed by three uncoupled elastic contributions of radial collagen fibers, circumferential collagen fibers, and an equivalent isotropic matrix. The model is calibrated using literature data through the inverse method. Simulation results indicate that specific collagen fibers alignment is responsible for the significant spatial and directional variation of deformation of the TM strip. With the appropriate strength criteria related to fiber deformation, the anisotropic localized failure mode of the TM strip observed in the experiment can be captured. The nonlinear nature and rotation of collagen fiber bundles are the origin of the nonlinear mechanical behavior of TM strips under uniaxial loading. The mesoscale constitutive model offers a different perspective on TM’s anisotropic and nonlinear elastic mechanical behavior. This research improves our understanding of the mechanical behavior of the TM and could help biomimetic graft development.

摘要

鼓膜是听觉系统的重要组成部分, 位于外耳道末端, 是一种含胶原的多层软组织膜. 鼓膜的纤维沿着径向和环向方向高度取向, 其独特而复杂的超微结构使得力学行为呈现各向异性非线性, 这对于声音传输很重要. 然而, 同时包含这两个特征的鼓膜本构模型尚 未提出. 在本研究中, 我们建立了考虑鼓膜纤维分布的细观本构模型, 模型能够同时捕捉各向异性和非线性弹性力学行为. 鼓膜被认为 是包含两族胶原纤维的连续纤维增强复合材料, 并通过整合沿厚度方向异质材料性质建立整体力学性质. 均匀化的力学性质被假定沿 着厚度方向均匀分布, 并由径向胶原纤维, 环向胶原纤维和等效各向同性基质的三个非耦合弹性贡献叠加组成. 通过逆方法并使用文 献数据校准模型. 仿真结果表明, 特定的胶原纤维排列是鼓膜条带试样变形呈现显著空间非均匀性及各向异性的原因. 通过与纤维变 形相关的强度准则, 可以捕获在实验中观察到的鼓膜条带各向异性局部化失效模式. 胶原纤维束的旋转和非线性性质是单轴加载下鼓 膜条带非线性力学行为的起源. 该细观本构模型为鼓膜的各向异性和非线性弹性力学行为提供了不同的视角. 这项研究提高了我们对 鼓膜力学行为的理解, 并有助于仿生移植物的发展.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant Nos. 11972205, 11921002, and 11972210).

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Authors and Affiliations

  1. School of Aerospace Engineering, Tsinghua University, Beijing, 100084, China

    Shuyi Xiang  (向书毅), Zhibo Du  (杜智博), Huibin Shi  (施汇斌), Ziming Yan  (严子铭) & Zhanli Liu  (柳占立)

  2. Department of Mechanics and Tianjin Key Lab of Nonlinear Dynamics and Control, Tianjin University, Tianjin, 300072, China

    Yongtao Sun  (孙永涛)

  3. Department of Otorhinolaryngology Head and Neck Surgery, Beijing Tongren Hospital, Capital Medical University, Beijing, 100730, China

    Jie Wang  (王杰)

  4. Beijing Engineering Research Center of Audiological Technology, Beijing, 100730, China

    Jie Wang  (王杰)

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  1. Shuyi Xiang  (向书毅)
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  7. Zhanli Liu  (柳占立)
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Contributions

Author contributions Shuyi Xiang Conceptualization, Methodology, Data curation, Validation, Formal analysis, Writing–original draft. Zhibo Du Methodology, Data curation, Software, Formal analysis. Huibin Shi Investigation, Resources, Validation. Ziming Yan Methodology, Software. Yongtao Sun Resources, Validation. Jie Wang Resources, Validation. Zhanli Liu Conceptualization, Methodology, Funding acquisition, Supervision, Writing–review & editing.

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Correspondence to Zhanli Liu  (柳占立).

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Xiang, S., Du, Z., Shi, H. et al. A fiber-reinforced mesoscale constitutive model of tympanic membrane considering anisotropic deformation. Acta Mech. Sin. 40, 623590 (2024). https://doi.org/10.1007/s10409-024-23590-x

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